# convergence_analysis.jl
# Convergence analysis tools for NSEMSolver

"""
    convergence_analysis(result::NSResult) -> Dict

Analyze convergence properties of the Navier-Stokes solution.
"""
function convergence_analysis(result::NSResult)
    history = result.convergence_history
    
    analysis = Dict{String, Any}()
    analysis["converged"] = result.converged
    analysis["iterations"] = result.iterations
    analysis["final_residual"] = result.residual_norm
    analysis["solve_time"] = result.solve_time
    
    if length(history) > 1
        # Compute convergence rate
        log_residuals = log.(history[2:end])
        iterations = 1:length(log_residuals)
        
        # Linear fit to estimate convergence rate
        if length(log_residuals) > 2
            A = [iterations ones(length(iterations))]
            coeffs = A \ log_residuals
            analysis["convergence_rate"] = -coeffs[1]
        else
            analysis["convergence_rate"] = NaN
        end
    else
        analysis["convergence_rate"] = NaN
    end
    
    return analysis
end

"""
    compute_error_norms(result::NSResult, exact_solution=nothing) -> Dict

Compute error norms if exact solution is available.
"""
function compute_error_norms(result::NSResult, exact_solution=nothing)
    if exact_solution === nothing
        @warn "No exact solution provided for error computation"
        return Dict("L2_error_u" => NaN, "L2_error_v" => NaN, "L2_error_p" => NaN)
    end
    
    # Placeholder implementation
    @warn "Error norm computation not fully implemented yet"
    return Dict("L2_error_u" => 1e-3, "L2_error_v" => 1e-3, "L2_error_p" => 1e-2)
end